Answer to Question #85032 in Electricity and Magnetism for Ajay

Question

in a one-dimensional device, the charge density is given by pv = po*x/a. If E = 0 at x = 0 and V = 0 at x = a, find v and E

Answer 1

1)

E=∫▒ρdx=∫▒〖(ρ_0 x)/a dx〗=ρ_0/a x^2/2+c

E(0)=0=c

Thus,

E=∫▒ρdx=∫▒〖(ρ_0 x)/a dx〗=ρ_0/a x^2/2

2)

V=-∫▒Edx=-∫▒〖ρ_0/a x^2/2 dx〗=-ρ_0/a x^3/6+c

V(a)=0=-ρ_0/a a^3/6+c

c=ρ_0/a a^3/6

Thus,

V=ρ_0/6a(a^3-x^3)